mirror of
https://github.com/fluencelabs/musl
synced 2025-06-29 22:51:55 +00:00
c599f4f4d7
for these functions f(x)=x for small inputs, because f(0)=0 and f'(0)=1, but for subnormal values they should raise the underflow flag (required by annex F), if they are approximated by a polynomial around 0 then spurious underflow should be avoided (not required by annex F) all these functions should raise inexact flag for small x if x!=0, but it's not required by the standard and it does not seem a worthy goal, so support for it is removed in some cases. raising underflow: - x*x may not raise underflow for subnormal x if FLT_EVAL_METHOD!=0 - x*x may raise spurious underflow for normal x if FLT_EVAL_METHOD==0 - in case of double subnormal x, store x as float - in case of float subnormal x, store x*x as float
40 lines
837 B
C
40 lines
837 B
C
#include "libm.h"
|
|
|
|
/* sinh(x) = (exp(x) - 1/exp(x))/2
|
|
* = (exp(x)-1 + (exp(x)-1)/exp(x))/2
|
|
* = x + x^3/6 + o(x^5)
|
|
*/
|
|
double sinh(double x)
|
|
{
|
|
union {double f; uint64_t i;} u = {.f = x};
|
|
uint32_t w;
|
|
double t, h, absx;
|
|
|
|
h = 0.5;
|
|
if (u.i >> 63)
|
|
h = -h;
|
|
/* |x| */
|
|
u.i &= (uint64_t)-1/2;
|
|
absx = u.f;
|
|
w = u.i >> 32;
|
|
|
|
/* |x| < log(DBL_MAX) */
|
|
if (w < 0x40862e42) {
|
|
t = expm1(absx);
|
|
if (w < 0x3ff00000) {
|
|
if (w < 0x3ff00000 - (26<<20))
|
|
/* note: inexact and underflow are raised by expm1 */
|
|
/* note: this branch avoids spurious underflow */
|
|
return x;
|
|
return h*(2*t - t*t/(t+1));
|
|
}
|
|
/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
|
|
return h*(t + t/(t+1));
|
|
}
|
|
|
|
/* |x| > log(DBL_MAX) or nan */
|
|
/* note: the result is stored to handle overflow */
|
|
t = 2*h*__expo2(absx);
|
|
return t;
|
|
}
|